My Teaching Philosophy:

My courses are based around encouraging students to actively think about how to arrive at a solution, while I guide them through the process of mathematical and logical reasoning. My objective is to demonstrate a central truth about mathematical thinking: the most productive way to approach a challenge is by thinking about what procedures are appropriate for a particular problem and in a particular context, not by simply knowing how to perform different procedures. I treat mathematics as a puzzle to be explored and played with. From the first day of the semester, I continually communicate to my students that there is no such thing as a “math person;” instead, mathematics is based around logic and reason, and logic and reason are central to what make us human. My hope is that in this way I can break down the math anxiety some students may have by transforming mathematics into an engrossing exploratory process.

For a detailed description of my teaching philosophy, please see my teaching statement.

Courses Taught at Penn State:

  • MATH 111: Techniques of Calculus II. (Spring 2020)
    • Multivariable functions; partial differentiation; multiple integrals; first-order linear and separable differential equations; applications.
  • MATH 220: Matrices. (Fall 2019)
    • Matrix algebra; linear transformations; subspaces; orthogonality; diagonalizability; characteristic polynomials; applications.
  • MATH 231: Calculus of Several Variables. (Spring 2019, Summer 2018*)
    • Three-dimensional analytic geometry; calculus of parametric curves; partial differentiation; applications.
  • MATH 230: Calculus and Vector Analysis. (Summer 2019*, 2018*; Spring 2018; Fall 2018, 2017)
    • Calculus of parametric curves, multivariable functions, and vector fields; multiple integrals; line and surface integrals; Green’s theorem, Stokes’ theorem, and the divergence theorem; applications.
  • MATH 251: Ordinary and Partial Differential Equations. (Spring 2017, Fall 2016)
    • First- and second-order equations; higher-order linear equations; Laplace transforms; systems of equations; Fourier series; partial differential equations.
  • MATH 110: Techniques of Calculus I. (Summer 2016)
    • Functions and graphs; techniques of differentiation and integration; improper integrals; applications.
  • MATH 021: College Algebra I. (Spring 2016)
    • Linear equations and inequalities; quadratic expressions; algebraic fractions; negative and rational exponents; radicals.

*These courses were taught online through Penn State World Campus.

Other educational experience:

  • Penn State University Department of Mathematics, MATH 141 Digital Teaching Assistant (Summer 2017)
    • Facilitated online discussion board and recitation sessions for online course in Calculus II.
  • Penn State University Department of Mathematics, MATH 022 Digital Teaching Assistant (Fall 2015)
    • Led online recitation sessions and graded assignments for online course in College Algebra II.
  • Hamilton College Department of Mathematics, MATH 337 Grader (Spring 2015)
    • Graded problem sets for upper-level undergraduate course in Partial Differential Equations.
  • Hamilton College Quantitative and Symbolic Reasoning Center, Peer Tutor (Fall 2012 – Spring 2015)
    • Tutored eight to twelve drop-in students a week in calculus, linear algebra, differential equations, general and organic chemistry, and biology.

Private tutoring:

In addition to teaching, I also privately tutor. While privately tutoring, I focus on developing a student’s independence in mathematical thinking. Just as when I teach classes, I believe critical thinking should take precedence over knowing facts. If you are interested in private tutoring, you can email me at dkv5049@psu.edu.